Batory 2LO Test 3 October 23, 2018
Imię i nazwisko:
Klasa:
Grupa 1 Wynik:
Question 1 (1 pt)
How many solutions does the equation ||x − 3| − 1| = 2 have?
A. 0 B. 2 C. 3 D. 4
Question 2 (1 pt)
If the line with the equation y −√
3x + 1 = 0 crosses the x-axis at the angle α, then
A. α = 30◦ B. α = 60◦ C. α = 120◦ D. α = 150◦
Question 3 (1 pt)
If the lines given by the equations y = 2x + m − 1 and y = (m − 1)x − m + 3 are parallel, then
A. m = 12 B. m = −12 C. m = 3 D. m = −3
Question 4 (1 pt)
For what values of m does the function f (x) = (m−3)x+m2−1 pass through the origin?
A. m ∈ {−1, 1} B. m ∈ R C. m ∈ (−∞, 3) D. (3, ∞)
Question 5 (1 pt)
The equation of the line that passes through (√
3, 1) and makes an angle of 120◦ with the x-axis is:
A. y =
√ 3
3 x B. y = −
√ 3
3 x + 2 C. y = −√
3x + 4 D. y = −x +√ 3 + 1
Batory 2LO Test 2, page 2 of 4 October 23, 2018
Question 6 (3 pts)
Consider the following system of equations:
2x − y = 4 − a x + y = a − 3
Find the set of values of a for which the solution (x, y) to this system lies in the III quadrant.
Question 7 (3 pts)
Find the coordinates of the point of intersection of f (x) = |x − 2| + |x + 2|
and g(x) = x + 3.
Batory 2LO Test 2, page 3 of 4 October 23, 2018
Question 4 (3 pts)
Find the number of solutions to the equation:
|x + 2| − |x − 3| = x + a depending on the parameter a.
Batory 2LO Test 2, page 4 of 4 October 23, 2018
Question 10 (5 pts)
Find the values of the parameter k for which the functions f (x) = 2x +k2 and g(x) = 3x − 2k intersect inside the triangle with vertices A(−2, 0), B(8, 0) and C(4, 6).